The total number of ways are formed is 4.43 x 10^10 by rounding to the hundredths place.
According to the statement
we have given that the some numbers of the songs which are added by the larrisa in her playlist.
And we have to tell the ways which are formed with the help of the combination and permutations.
So, For this purpose we know that the
The first condition we have given that the
"play no more than 4 blues songs" - indicates playlist can contain 0, 1, 2, 3, or 4 blues songs. You need to analyze five different cases and add them up together in the end. From 7 blues songs, you can either "pick" 0, 1, 2, 3, or 4. Since order matters, it's a permutation, not a combination.
Afterwards, it gets tricky. Consider the first case, where we have 0 blues songs. This means that there are 10 spaces for the remaining (3+5+7 = 15) songs, which means that they can be arranged in (7P0 ∙ 15P10) ways.
For the next case, where we have 1 blues songs, it means that there are 9 spaces for the remaining 15 songs, which means that they can be arranged in (7P1 ∙ 15P9) ways. Continue doing this for the cases of 2, 3, and 4 blues songs and add up all the cases together.
And from this way we get the all combinations which are formed.
So, For this purpose
n = (7P0 ∙ 15P10) + (7P1 ∙ 15P9) + (7P2 ∙ 15P8) + (7P3 ∙ 15P7) + (7P4 ∙ 15P6) = 4.43459016×1010,
which rounded to the hundredths place, is 4.43 x 10^10 possible playlists.
So, The total number of ways are formed is 4.43 x 10^10 by rounding to the hundredths place.
Learn more about the combination and permutations here
brainly.com/question/3901018
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